New results on asymptotic properties of likelihood estimators with persistent data for small and large T

Artūras Juodis () and Vasilis Sarafidis
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Artūras Juodis: University of Amsterdam

SERIEs: Journal of the Spanish Economic Association, 2023, vol. 14, issue 3, No 9, 435-461

Abstract: Abstract This paper revisits the panel autoregressive model, with a primary emphasis on the unit-root case. We study a class of misspecified Random effects Maximum Likelihood (mRML) estimators when T is either fixed or large, and N tends to infinity. We show that in the unit-root case, for any fixed value of T, the log-likelihood function of the mRML estimator has a single mode at unity as $$N\rightarrow \infty $$ N → ∞ . Furthermore, the Hessian matrix of the corresponding log-likelihood function is non-singular, unless the scaled variance of the initial condition is exactly zero. As a result, mRML is consistent and asymptotically normally distributed as N tends to infinity. In the large-T setup, it is shown that mRML is asymptotically equivalent to the bias-corrected FE estimator of Hahn and Kuersteiner (Econometrica 70(4):1639–1657, 2002). Moreover, under certain conditions, its Hessian matrix remains non-singular.

Keywords: Dynamic panel data; Maximum likelihood; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C13 C33 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13209-023-00286-y

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